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What is the value of y?

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What is the value of y? [#permalink] New post 02 Nov 2011, 12:11
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A
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Difficulty:

  95% (hard)

Question Stats:

38% (01:51) correct 62% (01:32) wrong based on 58 sessions
What is the value of y?

(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-y-127976.html
[Reveal] Spoiler: OA

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Re: What is the value of y? [#permalink] New post 02 Nov 2011, 13:37
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from 2nd we got 2 roots: -8 or 14, check this roots with 1st statement we see that 3|x^2-4| can't be negative, so -8 is out. 14 is left and it's the only choice left.
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Re: What is the value of y? [#permalink] New post 02 Nov 2011, 14:03
Thanks aaaqqq222. Much appreciated.
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Re: What is the value of y? [#permalink] New post 03 Nov 2011, 08:35
can somebody explain the question in detail. I understand the stmnt(2).
I solved stmnt (i) like this

3(x.x-4)=y-2
3x.x -12 =y-2
y=3x.x -10

by assigining "-" to absolute value

-3x.x +14=y
when equal 2 equations
14=-10.
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Re: What is the value of y? [#permalink] New post 03 Nov 2011, 11:20
Here is my take, can the experts confirm please if my approach is correct ?

1. 3|x^2-4|= y-2 gives us 2 values if we open the modulus, for the 2 values y = 3x^2 -10 and y = 14 – 3x^2. NOT SUFFICIENT.

2. |3-y|=11, gives y = -8, 14 if we open the modulus. NOT SUFFICIENT.

Combining 1 and 2. if we put the values y = -8, 14 in 3|x^2-4|= y-2,
If y = -8, 3|x^2-4|= -10, not possible as
If y = 14, 3|x^2-4|= 12, Only possible value.

Hence Ans is C.
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Re: What is the value of y? [#permalink] New post 12 Mar 2015, 07:19
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Re: What is the value of y? [#permalink] New post 12 Mar 2015, 08:39
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enigma123 wrote:
What is the value of y?

(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11


What is the value of y?

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(2) \(|3 - y| = 11\):

\(y<3\) --> \(3-y=11\) --> \(y=-8\);
\(y\geq{3}\) --> \(-3+y=11\) --> \(y=14\).

Two values for \(y\). Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-y-127976.html
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Re: What is the value of y?   [#permalink] 12 Mar 2015, 08:39
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